GCER Featured Research Profile Series
GU economists hold serve: New research by a team of GCER Fellows and grad students show how Federer, Djokovic, and Nadal can up their game.
Are the world’s best tennis pros playing winning strategies? In their recent paper, “Disequilibrium Play in Tennis” a team of Georgetown faculty and grad students, Axel Anderson, Jeremy Rosen, John Rust, and Kin-Ping Wong, conclude otherwise. They analyze the serve directions of top pros such as Roger Federer, Rafael Nadal, and Nolan Djokovic and conclude that by changing the directions they serve to, these pros can significantly increase their probability of winning the game. For example, they predict that by merely changing serve directions at different stages of the game, Roger Federer could increase his probability of winning the service game when serving to Rafael Nadal from 82% under Federer’s current serve strategy to 89% under the authors’ calculated “best response” serve strategy. For Djokovic serving to Nadal, the authors predict that Djokovic could increase his service game win chance from 84% to 93%.
Tennis serves are made to three key directions: “wide”, “to the body” or “down the T” and these serve directions are recorded for thousands of tennis matches in an online database called the Match Charting Project. The authors analyzed the probability that a given server wins a tennis game conditional on serving to different directions using this database. A key prediction of game theory, von Neumann’s celebrated Minimax Theorem, predicts that if a server randomizes across different serve directions, then the probability of winning conditional on serving to each of the three directions must be the same. The authors’ show that this fails to hold in tennis matches between top pro players, and then use dynamic programming to calculate the chances of winning with an optimal serve strategy given the observed win chances in the data. Even though the increase in the overall probability of winning the tennis game from serving to the direction with the highest win probability is small at any particular stage of the game, a best response strategy that consistently exploits these “one shot deviations” over all possible states in the game of tennis, results in cumulative increase in the probability of winning the overall game at the start of a tennis game that is much more significant, as the numerical predictions shown above indicate.
The size of the estimated increase in win chances contradicts a main prediction of traditional “rational” economic theory, namely that high ability, highly motivated economic agents should behave in accordance with game theory and its prediction that their strategies should constitute a Nash equilibrium. That is, there is no “deviation strategy” that should result in a higher payoff for any of the players in a game. The authors’ analysis suggests one possible explanation for their finding: namely, that professional tennis players have a distorted “mental model” of their own strengths and weaknesses and those of their opponent. The rapidly growing industry of “sports analytics” may help professional tennis players to adopt a more accurate statistical understanding of their own play and those of their opponents, and might ultimately lead to play that is more consistent with the predictions of von Neumanm’s Minimax Theorem, which is a special case (applied to two-person constant sum games) of the more general concept of Nash equilibrium in multiplayer, potentially non-constant sum games.
Previously Featured Research Profiles:
Spring 2021 Featured Research Profile: Finance-Thy-Neighbor? Georgetown Economist Margit Reischer analyzes the macroeconomic implications of trade credit in supply chains.
Fall 2020 Featured Research Profile: Impactful differences and differential impacts: Georgetown Economist Louise Laage shows how to recover average effects in panels with unobserved and unexplained sources of heterogeneity.
Spring/Summer 2020 Featured Research Profile: Spouse and house? GCER Fellow Minsu Chang connects the dots between the two.
Spring/Summer 2019 Featured Research Profile: GCER Fellow Alexandre Poirier’s and Matthew Masten’s study of treatment effects carves out the circumstances under which circumstances carve out economic behavior.
Fall 2018 Featured Research Profile: “You’re [not] fired!”–GCER Fellow Toshi Mukoyama and Sophie Osotimehin explore the dynamic linkages between employment protection regulations and firms’ innovation decisions.
Winter/Spring 2017-2018 Featured Research Profile: Child Care in Reverse: GCER Fellow Ami Ko explores the subtle effects of informal health care on the long-term care insurance market.
Fall/Winter 2016-2017 Featured Research Profile: Markets with Search and Matching Frictions: Georgetown economists James Albrecht and Susan Vroman discuss directed search in the housing market.
Fall/Winter 2015-2016 Featured Research Profile: How (not) to run a bank: Georgetown economist Martin Ravallion examines World Bank successes and failures.
Spring/Summer 2015 Featured Research Profile: Leaning in,… sort of: Georgetown economist Mary Ann Bronson explores reasons why men and women make different post-secondary educational investments.
Fall 2014 Featured Research Profile: Carbon emissions make the global economy tipsy… Harrison and Lagunoff study a “business-as-usual” scenario in a tipping model.
Spring 2014 Featured Research Profile: Collateral Damage to Standard Economic Theory… GCER Fellow Dan Cao shows how incorrect beliefs can fuel a crisis.
Fall 2013 Featured Research Profile: Oh what a tangled web we weave… Anderson and Smith explore the dilemmas of deception.
Winter/Spring 2013 Featured Research Profile: Unintended Consequences in the Struggle for Equal Rights: Anderson and Genicot explore the surprising relationship between suicides and female property rights in India.
Fall 2012 Featured Research Profile: Gale and O’Brien sing the blues over Use-or-Lose!
Spring/Summer 2012 Featured Research Profile:”What a piece of work is a man! How noble in Reason! How infinite in faculties!” … But how much is he worth? Huggett and Kaplan provide an answer.
Winter 2012 Featured Research Profile: Happiness is in the air! Levinson uses happiness surveys to put a dollar value on air quality.
Fall 2011 Featured Research Profile: Junior, the Risky Investment, Grandma, the Insurance Contract, and other bedtime stories as told by Gete and Porchia.
Spring/Summer 2011 Featured Research Profile: Ludema, Mayda, and Mishra show that when firms talk, governments listen.
Winter 2011 Featured Research Profile: Bachmann and Bai examine the effects of wealth bias in the policy process.